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Control of axisymmetric resonant vibrations and self-heating of shells of revolution with piezoelectric sensors and actuators

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International Applied Mechanics Aims and scope

The coupled problem of forced vibrations and self-heating of thermoviscoelectroelastic shells of revolution with piezoceramic sensor and actuator under monoharmonic loading is solved. The temperature dependence of the complex characteristics of the passive and piezoactive materials is taken into account. The coupled nonlinear problem of thermoelectroelasticity is solved by time-marching integration, using discrete orhogonalization to integrate the equations of elasticity and explicit finite differencing to solve the heat conduction equation. The effect of the dimensions of the sensor and actuator and self-heating on the sensor voltage and on the active damping of forced vibrations of a circular plate under uniform monoharmonic transverse pressure is studied

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References

  1. S. K. Godunov, “Numerical solution of boundary-value problems for systems of linear ordinary differential equations,” Usp. Mat. Nauk, 16, No. 3, 171–174 (1961).

    MATH  MathSciNet  Google Scholar 

  2. Ya. M. Grigorenko and A. P. Mukoed, Computer-Aided Solution of Linear and Nonlinear Problems in the Theory of Shells [in Ukrainian], Lybid’, Kyiv (1992).

  3. V. G. Dubenets and V. V. Khil’chevskii, Vibrations of Damped Composite Structures [in Russian], Vol. 1, Vyshcha Shkola, Kyiv (1995).

    Google Scholar 

  4. V. G. Karnaukhov, T. V. Karnaukhova, and O. V. P’yatets’ka, “Effect of the self-heating temperature on the active damping of forced axisymmetric vibrations of a circular plate with a piezoelectric actuator,” Visn. Kyiv. Univ., Ser. Fiz.-Mat. Nauky, No. 3, 107–114 (2004).

  5. V. G. Karnaukhov, T. V. Karnaukhova, and O. V. P’yatets’ka, “Effect of the self-heating temperature on the piezoelectric sensor of a circular plate undergoing forced axisymmetric vibrations,” Visn. Kyiv. Univ., Ser. Fiz.-Mat. Nauky, No. 1, 107–113 (2004).

    Google Scholar 

  6. V. G. Karnaukhov and I. F. Kirichok, Coupled Problems for Viscoelastic Plates and Shells [in Russian], Naukova Dumka, Kyiv (1986).

    Google Scholar 

  7. V. G. Karnaukhov, V. I. Kozlov, and T. V. Karnaukhova, “Refined thermomechanical model of composite Timoshenko-type shells with distributed transversely isotropic sensors under monoharmonic loading,” Mat. Met. Fiz.-Mat. Polya, 49, No. 4, 119–132 (2006).

    MATH  Google Scholar 

  8. V. G. Karnaukhov, V. I. Kozlov, and T. V. Karnaukhova, “Refined thermomechanical model of composite Timoshenko-type shells with distributed transversely isotropic actuators under monoharmonic loading,” Prikl. Pobl. Mekh. Mat., No. 4, 84–95 (2006).

  9. V. G. Karnaukhov, V. I. Kozlov, Ya. O. Zhuk, and T. V. Karnaukhova, “Coupled thermoelastic theory of layered shells with passive physically nonlinear inelastic layers and distributed inclusions for control of nonstationary vibrations,” Mat. Met. Fiz.-Mat. Polya, 44, No. 3, 96–106 (2001).

    MATH  Google Scholar 

  10. V. G. Karnaukhov, A. V. Kozlov, and E. V. Pyatetskaya, “Active damping of the vibrations of a rectangular plate with distributed sensors and actuators,” Teor. Prikl. Mekh., 37, 137–140 (2003).

    Google Scholar 

  11. V. G. Karnaukhov, V. I. Kozlov, and O. V. P’yatets’ka, “Active damping of axisymmetric resonant vibrations of a circular plate with piezoelectric inclusions,” Visn. Kyiv. Univ., Ser. Fiz.-Mat. Nauk, No. 2, 81–85 (2003).

    Google Scholar 

  12. V. G. Karnaukhov, V. I. Kozlov, and O. V. P’yatets’ka, “Contribution of boundary conditions to the active damping of the vibrations of a viscoelastic rectangular plate with distributed piezoelectric inclusions,” Visn. Kyiv. Univ., Ser. Fiz.-Mat. Nauky, No. 1, 75–85 (2003).

  13. V. G. Karnaukhov and V. V. Mikhailenko, Nonlinear Thermomechanics of Piezoelectric Inelastic Bodies under Monoharmonic Loading [in Russian], ZhGTU, Zhitomir (2005).

    Google Scholar 

  14. I. F. Kirichok, O. V. P’yatets’ka, and M. V. Karnaukhov, “Flexural vibrations and self-heating of a viscoelastic circular plate with piezoelectric actuators under electromechanical monoharmonic loading,” Visn. Kyiv. Univ., Ser. Fiz.-Mat. Nauky, No. 2, 84–92 (2006).

  15. V. V. Matveev, Damping of the Vibrations of Deformable Bodies [in Russian], Naukova Dumka, Kyiv (1985).

    Google Scholar 

  16. A. D. Nashif, D. J. Johnes, and J. P. Henderson, Vibration Damping, John Wiley & Sons, New York (1985).

    Google Scholar 

  17. N. P. Nesterenko, O. P. Chervinko, and I. K. Senchenkov, “Modeling the ultrasonic heating in structural elements of polymeric fibrous composites under normal loading,” Vest. Nats. Tekhn. Univ. “KhPI,” No. 9, 3–8 (2002).

  18. N. A. Shul’ga and A. M. Bolkisev, Vibrations of Piezoelectric Bodies [in Russian], Naukova Dumka, Kyiv (1990).

    Google Scholar 

  19. S. Belouettar, L. Azrar, E. M. Daya, V. Laptev, and M. Potier–Ferry, “Active control of nonlinear vibration of sandwich piezoelectric beams,” Comput. Struct., 86, 386–397 (2008).

    Article  Google Scholar 

  20. U. Gabbert and H. S. Tzou, Smart Structures and Structronic Systems, Kluwer, Dordrecht (2001).

    Book  Google Scholar 

  21. V. G. Karnaukhov, I. F. Kirichok, and M. B. Karnaukhov, “The influence of dissipative heating on active vibration damping of viscoelastic plates,” J. Eng. Math., 61, No. 2–4, 399–411 (2008).

    Article  MATH  Google Scholar 

  22. T. V. Karnaukhova and E. V. Piatetskaya, “On the basic relationships of thin termoviscoelastic plates with distributed actuators under monoharmonic loading,” J. Appl. Mech., 45, No. 2, 200–214 (2009).

    Google Scholar 

  23. I. F. Kirichok, “On the bending vibrations and heating of a ring plate with piezoceramic thin strips under fixed-freguency electromechanical loading,” J. Appl. Mech., 44, No. 2, 200–207 (2008).

    Google Scholar 

  24. I. F. Kirichok, “Resonance vibrations and heating of electromechanically loaded ring plates with piezoactuators with allowance for the shear deformation,” J. Appl. Mech., 45, No. 2, 215–222 (2009).

    Google Scholar 

  25. I. F. Kirichok and M. V. Karnaukhov, “One-frequency vibrations and vibration thermal heating of a three-layer piezoactive circular plate under electro-mechanical mono-harmonig loading,” J. Appl. Mech., 44, No. 1, 65–72 (2008).

    Google Scholar 

  26. I. F. Kirichok and M. V. Karnaukhov, “Monoharmonic vibrations and vibroheating of electromechanically loaded circular plate with piezoelectric actuators with allowance for the shear deformations,” J. Appl. Mech., 44, No. 9, 1041–1049 (2008).

    Google Scholar 

  27. H. S. Tzou and G. L. Anderson (eds.), Intelligent Structural Systems, Kluwer, Dordrecht (1992).

    Google Scholar 

  28. H. S. Tzou, Piezoelectric Shells (Distributed Sensing and Control of Continua), Kluwer, Dordrecht (1993).

    Google Scholar 

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Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterova St., Kyiv, Ukraine, 03057

    I. F. Kirichok

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  1. I. F. Kirichok
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Correspondence to I. F. Kirichok.

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Translated from Prikladnaya Mekhanika, Vol. 46, No. 8, pp. 42–57, August 2010.

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Kirichok, I.F. Control of axisymmetric resonant vibrations and self-heating of shells of revolution with piezoelectric sensors and actuators. Int Appl Mech 46, 890–901 (2011). https://doi.org/10.1007/s10778-011-0379-8

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  • DOI: https://doi.org/10.1007/s10778-011-0379-8

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